Optical potential for 12C + 28Si scattering

¹²C + ²⁸Si elastic scattering angular distributions are smooth functions, relatively easily fit by optical potential predictions, at laboratory bombarding energies, E_1ab, within ≈ 10 MeV of the Coulomb barrier (i.e. up to E_1ab ≈ 27 MeV). Between E_1ab = 27 and 36 MeV the angular distributions show pronounced oscillatory structure which is not easily fit with an optical potential. No optical potential has been found to give a very good account of all the angular distributions simultaneously; the best simultaneous fit to all the data was achieved with a surface-transparent potential whose real and imaginary well depths are energy dependent.     

The 12C+24Mg elastic scattering: An example of anomalous transparency at coulomb barrier energies

Fifteen complete angular distributions of the elastic scattering of ¹²C+²⁴Mg were measured at energies around the Coulomb barrier (E_cm = 10.67–16 MeV). The angular distributions are strongly oscillating and could be well described by an optical potential family, whose real part was determined without continuous ambiguity. The imaginary part of this optical potential is very shallow. At four energies the inelastic scattering angular distributions leading to the 2⁺ state of the ²⁴Mg were also measured and analysed with coupled-channels calculations. The volume integrals of the optical potentials used in the coupled-channels calculations present the threshold anomaly in their energy dependence, with a clear Q-value dependence.     

Excitation Function for 12C+12C Elastic Scattering

An energy dependent optical potential for ¹²C+¹²C system is established based on the analyses of the angular distributions of the elastic scattering in the energy range of 70-160MeV. This potential can well reproduce the excitation function for 12C+12C elastic scattering in the same energy range.     

Sub-coulomb energy 12C + 10, 11B and 14N + 10B fusion cross sections

Total fusion cross sections have been measured for the following reactions and energy intervals: ¹²C + ¹⁰B, E_c.m. = 2.10–5.38 MeV; ¹²C + ¹¹B, E_c.m. = 2.10–5.99 MeV; ¹⁴N + ¹⁰B, E_c.m. = 2.64–5.97 MeV. Absolute cross sections were extracted from the prompt γ-rays emitted by the various residual nuclei and measured by two large NaI detectors. No resonance structure was observed in the three reactions. The elastic scattering excitation function was also measured at θ_c.m. = 90.4° for ¹²C + ¹⁰B over the energy range E_c.m. = 3.18–6.82 MeV. Optical model potentials were found which could consistently describe both the fusion and elastic scattering data.     

Resonant Structure Described by a Deep Folded Potential for the 12C+12C Scattering at Lower-Energy Region

Based on the analyses of the elastic angular distributions,an energy-dependent folding potential for the 12C+12C system is established.This potential has a deep real part,and can reasonably well describe the resonant structure in the 12C+12C elastic scattering in the low-energy region of 10 ～ 70 MeV.     

Detailed energy dependence of the elastic and inelastic12C +12C scattering between 5 and 10 MeV/nucleon

Excitation functions for¹²C+¹²C elastic and inelastic scattering to 2⁺ level have been measured over the energy range 30–60 MeV (cm) by 250 keV steps using the kinematical coincidence method. The intermediate structure resonances disappear aboveE _cm=35 MeV while the broad and irregular structure becomes a general feature of the interaction at higher energies.     

Evidence of non-statistical structures in the elastic and inelastic scattering of58Ni+58Ni and58Ni+62Ni and intermediate dinuclear states

Excitation functions and angular distributions of⁵⁸Ni+⁵⁸Ni and⁵⁸Ni+⁶²Ni scattering at energies just above the Coulomb barrier have been measured aroundθ _cm=90° in energy stepsΔE _cm=0.25 MeV fromE _cm ? 110 MeV toE _cm ? 120 MeV for⁵⁸Ni+⁵⁸Ni and fromE _cm ? 110 MeV toE _cm ? 118 MeV for⁵⁸Ni+⁶²Ni. Evidence for structure of non-statistical character has been found in the angle-summed excitation functions; this evidence is corroborated by the analysis of the angular distributions. This is the first time that non-statistical structure in elastic and inelastic scattering is reported with high confidence level for this mass and excitation energy ranges. Attempts are presented to understand the nature of this structure, including the presence of intermediate dinuclear states and virtual states in a potential well.     

Alpha scattering from nonclosed shell nucleus 12C and alpha-nucleus interaction

In order to understand the α-nucleus interactions for the α+¹²C～α+¹⁶O systems systematically, α scattering from ¹²C is studied in a microscopic coupled-channel model using a folding potential and realistic microscopic wave functions of ¹²C. The experimental angular distributions of elastic and inelastic scattering to the 2⁺(4.43 MeV), 3^? (9.64 MeV), and 0 ₂ ⁺ (7.66 MeV) states in the range of E _α = 41–172.5 MeV are analyzed.     

Investigation of α-nucleus interaction in the 27Al (α,α)27Al scattering and 27Al (α, d )29Si reaction

Full finite-range macroscopic calculations in the distorted-wave Born approximation have been performed using the molecular and Michel α-nucleus potentials to analyze the angular distributions of cross-sections of the ²⁷Al(α, d)²⁹Si reaction, at 26.5 and 27.2 MeV incident energies, leading to seven transitions up to the excitation energy E _X = 4.08 MeV of the final nucleus. The parameters of the two types of the α-nucleus potentials are determined from the elastic-scattering data. Both the molecular and Michel potentials, without any adjustment to the parameters needed to fit the elastic-scattering data, are able in most cases to reproduce, simultaneously, the absolute cross-sections particularly at large angles, where the previous calculations failed to reproduce by orders of magnitude, and the gross pattern of angular distributions of the reaction. The deuteron-cluster spectroscopic factors for most of the seven transitions, deduced using the two α-²⁷Al potentials, differ from those obtained in earlier works. The spectroscopic factor for the ground-state transition, deduced in the present work for the 25.8 MeV data, agrees well with the shell model prediction. Received: 15 July 2002 / Accepted: 8 August 2002 / Published online: 10 December 2002 RID="a" ID="a"e-mail: akbasak2001@Yahoo.com Communicated by G. Orlandini     

The energy dependence of fusion in the 9Be+28Si system

The angular distributions of the energy spectra of the light charged particles (p, d and α) from the ⁹Be + ²⁸Si reaction have been measured in the energy range 12 ≦ E_lab ≦ 30 MeV. The particle evaporation spectra and the angular distributions were analyzed with a spin dependent statistical model. Angular distributions of ⁹Be ions elastically scattered on ²⁸Si have been measured at the energies 12 MeV, 17 MeV, 23 MeV and 30 MeV and were analysed, together with previously measured cross sections, with the optical model. The fusion cut-off angular momentum l_fus(E), the fusion cross section σ_fus(E) and the ratio σ_fus/σ_R^OM(E) were deduced. The excitation function for fusion was analyzed with the Glas and Mosel model. The parameters obtained from the fusion excitation function were compared with the corresponding ones from the ⁹Be + ²⁸Si optical-model interaction potential.     

Scattering and reactions of 14C + 14C and 14C + 14C

We have studied elastic scattering, inelastic scattering and several transfer channels of the systems ¹⁴C + ¹⁴C and ¹⁴C + ¹²C over a wide range of energies up to E_c.m. = 35 eMeV and 32 MeV, respectively. The reaction channels were identified by means of kinematic coincidences between solid-state detectors, γγ coincidences were measured to determine cross sections for mutual inelastic scattering of ¹⁴C + ¹⁴C.Pronounced regular gross structures, similar to those found for ¹⁶O + ¹⁶O, are observed in the elastic excitation function of ¹⁴C + ¹⁴C at θ_c.m. = 90°, The angular distributions measured at the energies of the maxima and an optical-model analysis suggest that one or a few surface partial waves dominate the scattering behaviour. Correlated structure of narrower width is found in the inelastic channels and, to a lesser degree, in the transfer channels which appear with rather small cross sections.In ¹⁴C + ¹²C elastic scattering the gross structures are strongly fragmented, in contrast to ¹⁴C + ¹⁴C but similar to ¹²C + ¹²C. While the ¹²C(2⁺) excitation is very weak, the observed strengths of the ¹⁴C(3^?) excitation and of neutron transfer point to a substantial role of these channels as coupling partners to the elastic configuration and to their influence on the elastic scattering behaviour. A correlated intermediate structure is observed near 23.5 MeV, where a dominance of l = 18 is suggested by the elastic scattering angular distribution. This unexpectedly high l-value exceeds l_graz at this energy by at least two units of ?.     

Fusion, resonances and scattering in12C+12C reaction

The variation of fusion cross-section (σJ_fus) with energy in the¹²C+¹²C collision is linked to the underlying resonance phenomenon through the behavior of reaction cross-section (σ) of which σ_fus is taken as a part. The calculation of σ_fus is done through an energy-dependent imaginary potential in the optical model potential (OMP). Through dispersion relation, such an imaginary potential gives rise to energy-dependent real potential which is incorporated in the OMP. In our calculation, a form of potential for the nuclear part which has a soft repulsive in-built core is introduced based on similar works done earlier. The calculated results of σ_fus are used to explain the oscillatory structure, astrophysical S-factor and the decreasing trend at higher energies of the experimental σ_fus data in the case of¹²C+¹²C system with remarkable success. The potential used for fusion calculation is tested for fitting elastic scattering data at some energies and is found good in forward angles. Further improvement of the fitting of these data is obtained by incorporating a coupling potential in the surface region. About twenty resonances are observed in our calculation in the specific partial waves and some of them are found close to the experimentally identified resonances in¹²C+¹²C reaction. Thus, we provide an integrated and comprehensive analysis of fusion, resonance and scattering data in the best studied case of¹²C+¹²C reaction within the framework of optical potential model.     

12C + 7Li Reaction measurements and the 12C(7Li,t)16O reaction

A measurement of the residues from the ¹²C + ⁷Li reaction has been obtained for ⁷Li energies from 10 to 38 MeV. From these measurements the fusion cross sections and critical angular momenta for the ¹²C + ⁷Li system have been deduced. Cross sections for the ⁷Li(¹²C, t)¹⁶O reaction have been obtained for ¹²C energies from 54 to 62 MeV at θ_lab = 2.7°. The critical angular momenta obtained from the fusion cross sections have been used to perform Hauser-Feshbach calculations for the ¹²C(⁷Li, t)¹⁶O reaction. These calculations have been compared to measured angular distributions over a wide energy range. By comparing the fusion cross sections required by the Hauser-Feshbach calculations to fit the ¹²C(⁷Li, t)¹⁶O(8.87 MeV) reaction and the measured residue cross section it is estimated that at least 80 % of the measured residues are fusion products. The calculations also indicate that direct processes dominate the population of many ¹⁶O levels at forward angles and the 10.35 MeV state at backward angles. The necessity for using a critical angular momentum in Hauser-Feshbach calculations is discussed.     

Coupled-channels analysis of energy-dependent isospin violation in the 12C(d, α)10B(1.74 MeV,T = 1) reaction

We have studied the isospin non-conserving ¹²C(d, α)¹⁰B(1.74 MeV, 0⁺, T= 1) reaction at several incident energies of 9 ≦ E_d ≦ 16 MeV in terms of a coupled-channels method. The reaction processes involved in the present analysis are the successive single-nucleon pick-up processes as well as the inelastic scattering of deuterons from ¹²C. It is assumed that the isospin violation should occur in the intermediate mirror cluster states of ³He + ¹¹B and t + ¹¹C, due to the Coulomb interaction. The calculation reproduces fairly well the observed features of the reaction, i.e. the decreasing cross section with increasing incident energy, and the variation of the angular distribution. We also note that the calculation shows the energy-dependent localization of isospin violation in the angular momentum space, i.e. a specifically narrow localization at the lower incident energies studied and its broadening at the higher energies. This fact is associated with the variation of the angular distribution from a forward-backward symmetry at the lower incident energies to a forward peak at the higher energies.     

Resonances and fluctuations in the 16O + 15N and 12C + 19F collisions

The search and study of quasi-molecular resonances in the ³¹P composite system populated via two entrance channels are performed with two different experimental techniques. The ¹⁶O + ¹⁵N reaction products have been studied by the γ-ray detection method at cm. energies ranging from 15.5 MeV to 36.1 MeV. Binary channels of the ¹⁶O + ¹⁵N and ¹²C + ¹⁹F collisions have been studied by using the kinematical coincidence method at 26 incident energies ranging from E_c.m. = 20.6MeV to 33.5MeV for the first system, and at energies corresponding to the same excitation energies of the composite system for the second system. The ¹⁶O + ¹⁵N reaction exhibits two prominent gross structures in the large angle elastic scattering excitation function correlated with the resonant structures observed in inelastic channel γ-ray yield measurements. Spin assignments were tentatively made for the two resonances. On the contrary, no such structures can be clearly established in the ¹²C + ¹⁹F system where only indications of non-correlated structures in various channels have been observed.     

Elastic and inelastic scattering of 185 MeV protons from 12C

The polarization of 185 MeV protons in elastic scattering and in the excitation of the 2⁺ state at 4.44 MeV and the 0⁺ state at 7.65 MeV in ¹²C has been measured in the angular region 2°–60°. Optical model calculations are performed for the elastic scattering. Angular distributions for the inelastic scattering from the 2⁺ state at 4.44 MeV and the 3^? state at 9.64 MeV are calculated in the distorted-wave impulse approximation (DWIA) as well as in the distorted-wave Born approximation (DWBA).     

Angular correlation studies of intermediate width structures in 16O + 12C

An angular correlation technique has been utilized to study the spins of several intermediate width resonances in the inelastic scattering of ¹⁶O + ¹²C in the range 19 ? E_cm ? 23 MeV. An analysis of the correlations and previously reported angular distributions strongly indicates that interpretations of these structures in terms of a single rotational band are inadequate.     

Folding model analysis of pion elastic and inelastic scattering from 6Li and 12C

π ^±-Nucleus scattering cross sections are calculated applying the Watanabe superposition model with a phenomenological Woods-Saxon potential. The phenomenological potential parameters are searched for π ^± scattering from ⁶Li and ¹²C to reproduce not only differential elastic cross sections but also inelastic and total and reaction cross sections at pion kinetic energies from 50 to 672 MeV. The optical potentials of ⁶Li and ¹²C are calculated in terms of the alpha particle and deuteron optical potentials. Inelastic scattering has been analyzed using the distorted waves from elastic-scattering data. The values of deformation lengths thus obtained compare very well with the ones reported earlier.     

Heavy ion reactions around the Coulomb barrier

The angular distributions of fission fragments for the ³²S+¹⁸⁴W reaction near Coulomb barrier energies are measured. The experimental fission excitation function is obtained. The measured fission cross sections are decomposed into fusion-fission, quasi-fission and fast fission contributions by the dinuclear system (DNS) model. The hindrance to completing fusion both at small and large collision energies is explained. The fusion excitation functions of ³²S+^90,96Zr in an energy range from above to below the Coulomb barrier are measured and analyzed within a semi-classical model. The obvious effect of positive Q-value multi-neutron transfers on the sub-barrier fusion enhancement is observed in the ³²S+⁹⁶Zr system. In addition, the excitation functions of quasi-elastic scattering at a backward angle have been measured with high precision for the systems of ¹⁶O + ²⁰⁸Pb, ¹⁹⁶Pt, ¹⁸⁴W, and ^154,152Sm at energies well below the Coulomb barrier. Considering the deformed coupling effects, the extracted diffuseness parameters are close to the values extracted from the systematic analysis of elastic and inelastic scattering data. The elastic scattering angular distribution of ¹⁷F+¹²C at 60 MeV is measured and calculated by using the continuum-discretized coupled-channels (CDCC) approach. It is found that the diffuseness parameter of the real part of core-target potential has to be increased by 20% to reproduce the experimental result, which corresponds to an increment of potential depth at the surface region. The breakup cross section and the coupling between breakup and elastic scattering are small.